فهرست مطالب

Mathematical Modeling - Volume:7 Issue: 4, 2019
  • Volume:7 Issue: 4, 2019
  • تاریخ انتشار: 1398/09/10
  • تعداد عناوین: 6
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  • Hamideh Nasabzadeh * Pages 337-347
    In this paper, based on the single-step Hermitian and Skew-Hermitian (SHSS) iteration method [C.-X. Li, S.-L. Wu, A single-step method for non-Hermitian positive definite linear systems, Appl. Math. Lett. 44 (2015) 26-29] and by using the generalized Taylor  expansion method for solving linear systems [F. Toutounian, H. Nasabzadeh, A new method based on the generalized Taylor expansion for computing a series solution of linear systems, Appl. Math. Comput. 248 (2014) 602-609], a new method (GT-SHSS) is introduced to solve non-Hermitian positive definite linear systems. The convergence properties of the new method are discussed. We show that by using suitable parameters, the GT-SHSS iteration method is faster than the corresponding SHSS iteration method. The numerical examples confirm the effectiveness of the new method.
    Keywords: Non-Hermitian, HSS method, convergence Analysis, iterative Method
  • Zuber Akhter *, S.M.T.K. Mirmostafaee, Haseeb Athar Pages 381-398
    In this paper, we obtain  new explicit expressions for the single and product moments of order statistics from the standard two-sided power (STSP) distribution. These expressions can be used to compute the means, variances and the covariances of order statistics from the STSP distribution. We also have a glance at the application of the results  to the lifetimes of the coherent systems.  Two real data examples are given to illustrate the flexibility of the STSP distribution.
    Keywords: Coherent systems, explicit expressions, product moments, standard two-sided power distribution
  • Majid Erfanian *, Hamed Zeidabadi Pages 399-416
    We present a method for calculating the numerical approximation of the   two-dimensional mixed Volterra Fredholm integral equations, using the properties of the rationalized Haar (RH) wavelets and the matrix operator.  Attaining this purpose, first, an operator and then an orthogonal projection should be defined. Regarding the characteristics of Haar wavelet, we solve the integral equation without using common mathematical methods. An upper bound and the convergence of the mentioned method have been proved, by using the Banach fixed point. Moreover, the rate of the convergence  method is  $O(n(2q) ^n)$. Finally, several examples of different kinds of functions are presented and solved by this method.
    Keywords: Nonlinear 2D mixed Volterra Fredholm integral equation‎, ‎Haar Wavelet‎, ‎Error estimation
  • Navid Pourjafari, Jalil Seifali Harsini * Pages 429-443
    Massive MIMO is known as a core technology for future 5G networks. The major advantage of massive MIMO over the conventional MIMO systems is that different mobile users are allowed to communicate in the same time-frequency resources while the resultant severe interferences can be eliminated using linear signal processing schemes. This is a consequence of the favorable propagation condition and channel hardening which are known as two basic limiting results in mathematics. In this paper we propose new stochastic convergence proofs for these limiting results in terms of the complete convergence in a massive MIMO system with uncorrelated Rayleigh fading.
    Keywords: Massive MIMO systems, favorable propagation condition, channel hardening, stochastic convergence, Rayleigh fading
  • Sunil S Kumbhar *, Sarita Thakar Pages 445-467
    In this paper second order explicit Galerkin finite element method based on cubic B-splines is constructed to compute numerical solutions of one dimensional nonlinear forced Burgers' equation. Taylor series expansion is used to obtain time discretization. Galerkin finite element method is set up for the constructed time discretized form. Stability of the corresponding linearized scheme is studied by using von Neumann analysis. The accuracy, efficiency, applicability and reliability of the present method is demonstrated by comparing numerical solutions of some test examples obtained by the proposed method with the exact and numerical solutions available in literature.
    Keywords: Forced Burgers' equation, cubic B-splines, Galerkin Finite Element Method, Taylor series, von Neumann analysis
  • Komeil Izadpanah *, Ali Mesforush, Ali Nazemi Pages 469-496
    In this paper, we propose a numerical method to solve the elliptic stochastic partial differential equations (SPDEs) obtained by Gaussian noises using an element free Galerkin method based on stabilized interpolating moving least square shape functions. The error estimates of the method is presented. The method is tested via several problems. The numerical results show the usefulness and  accuracy of the new method.
    Keywords: Element free Galerkin method, Stabilized interpolating moving least square, Stochastic elliptic equation Error estimates